Prime Minister Anker Jorgensen's Social Democrats easily retained power in economically troubled Denmark with a surprisingly strong showing in today's national election.

In what was seen here as a personal victory for Jorgensen, the left-of-center, union-based Social Democratic Party won 38 percent of the vote and increased its seats in the 179-seat Danish parliament from 65 to 69.

Its principal opposition, a right-of center coalition of the Conservation and 55 parliamentary seats. The rest of the parties, won 31 percent of the vote and Liberal parties along with two smaller seats divided among the five other parties scanning the Danish political spectrum.

Jorgensen, whose party may pick up another seat or two in later voting in Greenland and the Faroe Islands, is expected to form a minority government, quite possibly with the support of the smaller Socialist People's Party just to his left and the Radical Liberals just to his right. They each won 10 seats in parliament, and their leaders said they were ready to support a Social Democratic government if they could agree with Jorgensen on some key policies. Minority governments of this kind are common in Denmark's multiparty, proportional voting.

Jorgensen indicated late tonight that he also will seek the support in parliament of the Liberals, Conservatives and other right-of-center parties for drastic measures to cope with Denmark's continuing economic crisis.

"It will not be easy, but it will be possible," he said about building a consensus for austerity policies. He said he would start discussions Wednesday with leaders of all parties except the most radical leftist socialists and two tax-protest parties. Even the Liberal and Conservative leaders said they were ready to talk to him.

Since the early 1970s, the cost of maintaining Denmark's welfare state and the impact of soaring oil prices on its trade-dependent economy have produced huge budget and trade deficits, high inflation and unemployment and a growing threat to the Danes' comfortable standard of living. Jorgensen had tried unsuccessfully to reduce the deficits and slow double-digit inflation by steadily increasing Denmark's already high taxes and negotiating to hold down pay raises.

Although these efforts did not turn out to be strong enough, Jorgensen remained personally popular, according to opinion polls. A small, balding bearded man with an affable manner, he has been prime minister for six of the last seven years, Jorgensen, 57, who was orphaned when he was 2 and largely educated himself, rose through the union movement here from an unskilled laborer to union president and party leader. He was blamed for a bumbling start his first year as prime minister, which cost his party power for the next year. But he soon returned to office and endeared himself to many Danes with what they saw as a no-nonsense, common man's approach to government during a disillusioning time.

A year ago, Jorgensen dramatically moved to form an unusual coalition government of the Social Democrats and the Liberals. They agreed to try to win parliamentary approval for some kind of wage and price freeze to stop the inflationary spiral that is pricing Danish exports out of the world market.

But his party's union supporters insisted that the package include several union demands. The most significant of these were government subsidized jobs for the high number of unemployed, tax changed to decrease interest deductions claimed by wealthier Danes, and mandatory-sharing by Danish firms to enable their employes and the unions to eventually become "co-owners" of the business.

The Liberals would not agree to these policies and broke with the Social Democrats, forcing today's election. The Liberals, Conservatives and their two small right-of-center allies then campaigned collectively against the Social Democrats accusing them of being union-controlled and asking, "who rules Denmark?"

Jorgensen answered them during the campaign by saying, "Without trade union support, no incomes policy can be carried out successfully, nor any comprehensive solution to the economic crisis be reached." The Liberals held their ground in today's voting, winning 12.5 percent of the vote and 22 seats in parliament. These numbers were matched by Conservatives, who scored the biggest gain by increasing their proportion of the vote and seats in parliament by 50 percent.

The Conservatives in Sweden, Norway and Finland also made dramatic advances in elections in those Scandinavian countries this year. But Denmark's Conservatives, who similarly support but want to limit the growth of the Scandinavian welfare state, appear to have won many of their new voters from a tax-protest party, the Progress Party, which is still further to the right.

The Progress Party, which favors abolition of income tax and elimination of government bureaucracy, suffered its most serious setback since it was founded in 1973. Its share of the vote declining from 15 to 11 percent and its parliamentary seats dropping from 26 to 20.Its founder, Mogens Glistrup, a burly tax lawyer who became a celebrity by refusing to pay taxes, is appealing his conviction last year on charges of gross income tax invasion and fraud.